I am not an expert but I think it would be counter productive.

HOpe you feel better soon!

No expert here either, seems like it may be best to wait it out, tough decision though...

If I can get around, but I just feel tired, but not achy, I'll train for sure. I find that if I have a cold, I keep on my fishoil, garlic, vitamin C and probiotic regimen and keep exercising with *lots*, even sometimes more than usual the amount, of water.

I find I typically get over my colds quicker by doing this, but I also restrict myself to the gym, vs going outside specifically because it's a controlled environment where I can just get in the car and go home if I don't feel up to it.

Otherwise you may be doing yourself more harm than good. That said, if you do go to the gym, make sure you wipe everything down after you use it so as to help prevent others from getting your crud too.  

Hope this helps. And of course, if you're too sick to feel like going anywhere, try it once and if you can't manage, then you need to wait.